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End date: 2021 × Start date: 2020 × Type: Text × Version: publishedVersion × Subject: uniqueness × WGL Institute: WIAS ×

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Now showing 1 - 3 of 3
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    On the existence of weak solutions in the context of multidimensional incompressible fluid dynamics
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2021) Lasarzik, Robert
    We define the concept of energy-variational solutions for the Navier--Stokes and Euler equations. This concept is shown to be equivalent to weak solutions with energy conservation. Via a standard Galerkin discretization, we prove the existence of energy-variational solutions and thus weak solutions in any space dimension for the Navier--Stokes equations. In the limit of vanishing viscosity the same assertions are deduced for the incompressible Euler system. Via the selection criterion of maximal dissipation we deduce well-posedness for these equations.
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    Gibbs point processes on path space: Existence, cluster expansion and uniqueness
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2021) Zass, Alexander
    We study a class of infinite-dimensional diffusions under Gibbsian interactions, in the context of marked point configurations: The starting points belong to R^d, and the marks are the paths of Langevin diffusions. We use the entropy method to prove existence of an infinite-volume Gibbs point process and use cluster expansion tools to provide an explicit activity domain in which uniqueness holds.
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    Further regularity and uniqueness results for a non-isothermal Cahn--Hilliard equation
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2020) Ipocoana, Erica; Zafferi, Andrea
    The aim of this paper is to establish new regularity results for a non-isothermal Cahn--Hilliard system in the two-dimensional setting. The main achievement is a crucial L∞ estimate for the temperature, obtained by a suitable Moser iteration scheme. Our results in particular allow us to get a new simplified version of the uniqueness proof for the considered model.